7)sin x<1/2
½=sin 30 =sin(180-30)=sin 150
or, sin30<1/2
and sin 150 >1/2(why? And how?)
or, x belongs to (0,30) union (150,360) [given:
0<x<360]
I want a complete explanation.
8) Give the general soln of x:
log sin x (base cos x) +log cos x (base sin x) =2
on solving,
log sin x (base cos x) =1
or, sin x = cos x
or, tan x = 1 =tan (pi)/4
or, x = 2n(pi)+(pi)/4 (why 2n(pi)?)
when tan x = tan y
then x = n(pi) + y
-
UP 0 DOWN 0 0 2
2 Answers
62For the first question...
Just think of the graph of sin x..
That will give you the whole picture ...
Find teh range in 0 to 2 pi..
Then it will be periodic...
628) Give the general soln of x:
log sin x (base cos x) +log cos x (base sin x) =2
on solving,
log sin x (base cos x) =1
or, sin x = cos x
or, tan x = 1 =tan (pi)/4
or, x = 2n(pi)+(pi)/4 (why 2n(pi)?)
when tan x = tan y
then x = n(pi) + y
In this question, what you are saying is correct..
I did not understand what your question is!!!
If you want the explanation, the first step is the only one where there is something slightly not so obvious.. the first step is p/q+q/p = 2.
but we know by AM GM that x+1/x=2 has only one solutoin x=1
so log sinx(base cos x) = 1
hence log sin x / log cos x = 1
so log sin x = log cos x
so sin x = cos x (since log is a one one onto function)
hence the remaining part follows :)